BootstraptVerfahren

BootstraptVerfahren is a resampling-based statistical method used to assess the sampling distribution of a statistic and to estimate measures such as standard errors, confidence intervals, and bias. It relies on the idea that the observed data approximate the underlying population; by repeatedly drawing samples with replacement from the observed data, one can simulate the variability of the statistic without strong parametric assumptions.

Procedure: From an initial sample of size n, form many bootstrap samples by sampling with replacement. For each bootstrap sample, compute the statistic of interest. After a large number of resamples (often thousands), use the empirical distribution of the bootstrap statistics to estimate standard errors and construct confidence intervals, via percentile methods, bias-corrected and accelerated (BCa) intervals, or other bootstrap-based approaches.

Variants: The nonparametric bootstrap resamples the actual data; parametric bootstrap simulates from an estimated model; stratified bootstrap preserves group structure; block bootstrap variants address dependence in time series. There are also bootstrap-t methods that use a studentized statistic.

Applications and limitations: BootstraptVerfahren is widely used to assess uncertainty for means, medians, regression coefficients, and other statistics, especially when analytic formulas are complex or unavailable. It assumes the sample is representative of the population and can be biased for very small samples, highly skewed distributions, or strongly dependent data unless appropriate variants are used. Computational cost can be substantial, though modern computers mitigate this.

History and relation: The method originated with Bradley Efron's bootstrap in 1979 and has since become a standard tool in statistics, econometrics, and data science. The name reflects the idea of estimating variability by reusing the observed data.